Abstract
In [Trans. Amer. Math. Soc. 348 (4) (1996)], Blokh et al., studied the space of the
ω-limit sets
W
(
f
)
, produced by a continuous map on
I
=
[
0
,
1
]
, and established that endowed with the Hausdorff metric topology on
I, this space is compact. For general continuous maps on
I
2
, we show that this space is not compact and for maps whose
W
(
F
)
is included in a fiber of
I
2
, we present examples of both types: holding and not holding the property of being compact.